Transmission circuits



-pf' 1931 T. c. FRY 1,799,810

m TRANSMISSION CIRCUITS FiledDec." 5, 1928 3 Sheets-Sheet 1 www BY W

ATTORNEY April 7, 1931. 1 c, F'RY 11,799,810 y TRANSMISSION CIRCUITS Filed Dec. 5. 192%2v 5 Sheets-Sheet 2 Ffa-4 /N VENT 0l? i. BY

Patented pr. 7, 1931 UNITED STATES PATENT OFFICE THORNTON C. FRY, 0F WYOMING, NEW JERSEY, ASSIGNOR TO BELL TELEPHONE LABORATORIES, INCORPORATED, OF NEW YORK, N. Y., A CORPORATION OF NEW YORK TRANSMISSION CIRCUITS Application led December 5, 1928. Serial No. 323,880.

This invention relates to electrical wave transmission, and particularly to the correction of signal distortion in systems for the transmission of information, such as telephone or telegraph systems.

lVheninformation is transmitted by an electric current varying in accordance with a sequence of symbols the important requirement for intelligible reception is that the time variations of the received current should correspond to that of the current originally transmitted. If it does not the received signal is distorted and its intelligibility is diminished. From the viewpoint that a signal may be considered as comprising a multiplicity of simple harmonic waves of different frequencies, signal distortion may be described in terms of the effects produced on the several single frequency component waves as they traverse the system. In linear systems, that is, in systems in which the impedances of the elements are independent of the current strength, two types of distortion are recognized. First, the component waves of different frequency may be attenuated in different ratios, and second, the component waves may travel with different velocities, with the result that they arrive at the receiving end of the system with their relative phases altered. The first type is known as amplitude distortion, and the second type as phase, or velocity, distortion. Generally both types are present in the resultant signal distortion, but each separately may be effective to diminish the intelligibility of the signal. Where a transmission line is involved the wave propagation characteristicis dependent upon the resistance, inductance, leakance, and capacity of the line. If these quantities are properly related the line by itself may be distortionless, but in most, if not all, practical cases this proper relationship does not exist and the line is productive of both'amplitude distortion Aand phase distortion, In addition distortion may be introduced by discontinuities in the line which give rise to wave reflection.v Such discontinuities may be caused by the insertion in the line or at its terminals of apparatus having an impedance different from the characteristic impedance ofthe line.

Complete freedom from signal distortion requires that waves of all frequencies, from zero to infinity, be propagated with the same velocity and with the same degree of attenuation, but for many purposes it has been practical to limit the frequency range in which the requirements are met to such a value that only the most important of the component waves are transmitted with uniform velocity and attenuation. In telephone lines, for example, this has been accomplished by the use of loading coils. The added inductance of the coils serves to diminish both the amplitude distortion and the phase distortion in a certain rrange of frequencies, but at higher frequencies `the distortion is greatly increased by wave reflections at the points where the coils are inserted. The added inductance' is also effective to reduce the wave propagationv velocity in the frequency range in which the distortion is compensated. Continuous loading eliminates the wave refiec-tions and, if of proper magnitude, can render the line distortionless.

Another method of correcting distortion involves the use of networks which may be connectedto thel ends of a line, or inserted at intermediate points, to compensate either the amplitude distortion or the phase distortion or both. Vith the networks heretofore available the application of this method has been restricted to the compensation of distortion in a limited frequency range and to an approximate degree of accuracy, As the frequency range is widened and as the accuracy of the` compensation is increased the design of the networks tends to become very laborious and their construction complicated. By this invention compensating networks are provided, which, when combined with a given uniform transmission line, render the combination substantially completely distortionless. Amplitude distortion and phase distortion are corrected for all frequencies from Zero to infinity, and with a degree of accuracy as high as may be desired.

A feature of the invention is that the impedances constituting the compensating networks comprise ladder type structures or artificial lines, each branch of which is lmade up of simple combinations of elements, for example resistance and inductance, or resist- .ance `and capacity. No negative impedance elements are employed. For perfect compensation these ladder type lines should, theoretically, have an infinite number-of sections, but, for the reason that the cu rents are attenuated as they .penetrate into the lines, a high degree of compensation can be obtained by the use of a small number of sections. By the simple expedient of extending the lines to include a larger number of sections any desired degree of accuracy can be achieved.

Besides having a simple structural arrangement, the networks of the invention possess the advantages that they cause no wave reflection when inserted in the line they are designed to compensate, and are applicable to the correction of lines with or without distributed lshunt conductance, that is, they are adapt-ed to compensate the distortion in a line of the general type having distributed resistance, inductance, capacity, and conductance.

The `compensating networks of the invention may take various schematic forms. such as, for example, a three branch T or fr, or a four branch lattice. ln each case the branches consist of singly infinite ladder lines of the type mentionedabove, in which the impedances are all of a simple character involving only ,positive coeliticients.

ln the detailed description which follows the invention will be described with reference to a limited number of networks representative of the preferred forms. The geueral method of design will also be described whereby .the design and construction of other forms of network may be readily achieved. Of the drawings:

l represents in schematic form a compensated transmission line in accordance with the invention;

Figs. 2 and f3 represen-t the impedances constituting the branches of the compensating network in Fig. l;

Figs. 4 and 5 are charts for facilitating the design of the compensating networks;

Figs. 6 and 7 illustrate the impedances of a network o f the invention for the compensation of a particular line;

Figs. .8 and 9 illustrate the degree of `compensation attained in the particular example by the use of the structures of Figs. 6 and 7; and

Figs. l0 and ll illustrate additional forms of compensating network in accordance with the invention.

rhe system shown in Fig. l comprises a uniform line divided into a plurality of sections l0, ll, l2, etc., with each of which is associated a network 13, 14, etc., designed to compensate the distortion therein. The line may be regarded as being` loaded by the insertion of networks at intervals, and the combination of a line section and a compensating network may for convenience be termed a loading` section. The fundamenta-l requirements for the design of the compensating networks are readily established. First, in order that the networks may be inserted without introducing additional distortion due to wave reflection, their characteristic impedances must be the same as that of the line. Second. the attenuation and velocity characteristics of the networks must be complementary to vthose of the line sections respectively associated therewith so that the resultant attenuation and velocity may be constant.

Consider the loading section formed b v ie uniform line section l0 and the network The propagation constant, FZ, and the characteristic impedance Z. of the line section are given by the equations:

liuc coi ants, resistance, inductance, capacity and conductance per unit length, and l is and the length of the line section. The symbol o is the usual frequency factor, 2a times the frequency. In order that the loading section shall be distortionless its propagation constant should have the form otljcul where a and are both constant. The real part a of this expression represents the attenuation and its constancy corresponds to the absence of amplitude distortion. The imaginary part a represents the phase change of a wat-e in traversing the section, the factor being` the reciprocal of the wave velocity. Constancy of the velocity. therefore. corresponds to a linear relationship between the phase shift and the frequency. If desired values are assigned to a and the propagation constant of the compensating network becomes zx-ljw- F To avoid reflections the characteristic impedance of the network should be equal to Z.

Knowing the values -of the characteristic impedance and the propagation constant for lthe network, the 'Values of the impedances of the various branches can be established by well-known rules. `For a simple symmetrical T-network, as shown in the figure, comprising series impedances J1, and a shunt iinpedance J2, the values are 4 I i and '1 J2=Z cosech (a+jw-IZ). (4) Theseexpressions for the impedances are, -of course, not in a form that would enable a structure to be built having the'desired impedance values, but it will be shown that they can be transformed in such manner that they can be at once identified with a simple ladder type network.

It is well known that the impedance of a ladder, or series-shunt, type of network can be expressed as a continued fraction the elements of which are alternately the impedances of the series branches and the admittances of the shunt branches. The admittance is expressed by the reciprocal of this fraction, which is also a continued fraction of the same type. If, then, the expressions for J1 and J2, or for their reciprocals, can be expanded as continued fractions the elements of which can be identified alternately with the impedances and admittances of known combinations of electrical elements, it follows that structures may be built having` the impedances J1 and J2. Many such expansions are possible, but not all of them are practical. For example, the elements ofthe continued fraction may, in some cases, correspond to the impedances of infinitely extended networks of the ladder type and, since the continued fraction will in general have an infinite number of elements, the resulting impedance would be an infinite ladder type network each branch of which is also an infinite' ladder type network. In other cases, the elements of the expansion may represent simple impedance combinations, but may involve impedance elements having negative coeiiicients, for example negative resistance. Structures of this type may be realized, approximately at least, by the use of certain types of amplifier circuits, but, for the purposes of the present invention, a multiplicity of these would be required and the arrangement would be extremely complicated. For simplicity, therefore, it is necessaryrthat the. elements of the continued fractions into which the impedance functions are expanded should represent simple combinations of impedance elements all having positive coefficients, or', in other words, the elements should represent simple passive impedances. It is also necessary that the expansions should either have a finite number of terms or else should be convergent. Only the latter case need betconsidered since theexpressions for J1 and J 2 are of a type that can be expanded only as infinite seriesl or as infinite continued fractions. Y v 1 Under certain conditions a function F(y) canl be expanded as a convergent continued fraction ofthe type v in which the coefficients a0, al, etc., are all positive. These conditions refer to the mathematical properties of the function F(y) and are discussed at length by Perron, Die Lehre von den Kettenbrchen, B. G. Teubner, Leipzig, 1913, pages 396 to 417. Fractions of this type were originally studied by Stieltjes, Annales de la Faculte des Sciences de Toulouse, Volumes VIII and IX, and are known as Stieltj es fractions. If the function F expresses the frequency characteristic of animpedance, y being a function of frequency the continued fraction represents a series-shunt network by which the impedance can be realized. The series branches comprise resistances of valuesao, a2, etc., and the shunt then branches admittances of values aly, way, etc. The degree of complexity of the shunt branches depends on the form of y, expressed as a function of frequency.

In many cases the expression for the impedance may be incapable of expansion as a Stieltje-s fraction, that is to say, the impedi ance cannot be realized by a series-shunt network of the simple character described. For these cases a modified form of the Stieltjes fraction is often suitable. If the argument y is separable into two factors u and 0, it may be possible to expand the function u or the function .1 Y UF@ as a Stieltjes fraction. In the first, the eX- pansion would lead to Foi- @a+ 1 al@ -land in thesecond to l Fc) 1 aaa-l- 1 al@ -ll (7) Each .of these fractions can represent seriesshunt impedance structures provided Quand v are functions of frequency of the saine type 1as the impedances or admittances of known combinations of electrical elements.

The first step in the design of networks to represent J1 and J2 is to chan-ge the expressions for the impedances in terms of frequency into one or other of the forms where Q is a constant factor and the function FUMJ) is such that it can be expanded as a Stieltjes fraction. To simplify the appearance of the equations it is convenient to introduce a new notation in which L Z: ca -@WMM and 0R-.Le

In terms of this notation the impedai'ices of the T-network branches ybecome F me] e and J2= dm cosech jeg {gwen} (9) Further steps in the transformation require that definite values be assigned to a and the attenuation and .phase constants of the loading section. The propagation constant of the smooth line, given by Equation .(1), is a. complex quantity, the real and the imaginary components of which are both variable with frequency. The real component representing attenuation increases with frequency from the value at zero frequency to the value l RO+ L G at infinite frequency. The imaginary .component likewise ranges between the values RC+LG W at zero frequency and wl JL@ .at :infinite frequency. The velocity ofpropagation increases in the same man-ner :as .the

impedance functions that Ycan beeexpanded as Stieltjes fractions7 hut it is lmanifest th at lthe constant attenuation cannot he less than the ymaximum line attenuation. The choice of the uniform effective velocity is also restrict- .ed for the reason that a certain definite time i .interval is required for any wave to .traverse the uniform line and no network placed at the `end of the line can do anything to reduce lthis .time interval.

rllhe choice of the values of the attenuation and phase yconstants to lcorres-pond to the values of the uniform line constants at infinite frequency gives the following values Vfor a and which, if substituted in Equations (8) and ,(9), give and \/%J1= Vmccsech 0131+ atm]- (11) Introducing the further transformation g/:ztz-i-t), the following equations are obtained:

4 o' T* -smh 1 a QJZZ y@ 2(/y+1 w/), 13)

which express the impedanoes ras functions of y capable of expansion .as Stieltjes fractions. 'The values of J1 and J2 ldetermined from the expansion `are i inwhich the coeicients a0, a0', etc; are numerical quantities.

The procedure rfor the evaluation of t-he coeiiicients a0, al, a0', a1,.etc. is explained in my earlier Patent'1,57,0,215, issued January 19, 1926, in which the design of impedance network forother purposes is discussed. The

method of evaluation is also described in Perrons textbook referredto above. In the above expansions the coefiicients are functions of the quantity cr and therefore of the length Z of the section of uniform line that is to be compensated. The values of the irst seven coefiicients in theA expansion for J1 for different values of a are given by the curves of F ig. L1, and the'irst'six coefficients in the expansion for J2 are similarly -plotted in Fig. 5.

In theexpansion `for .I1-'the' first coeiiicient a0 has the constant value 2; the even coetlicients a2, a4, as, etc. have values which increase with a and which are sufficiently alike to be represented by a single curve; and the odd coefficients likewise converge towards a single constant. In the expansion for J2 the first coefcient a0 is Zero. The remaining coefficients are-positive for a range of values of a and athigher valuesvare negative. It may be shownthat solong as fr does not exceed the value a mV-1r all of the coeiiicients of the expansion are positive. Negative values of the coeiiicients would correspond toan impedance structure using negative elements and hence to one that could be Vrealized only' by the use of negative impedance devices such as amplifiers. In order that the network may be of the passive type it is necessary, therefore, that the uniform line sections should not exceed in length the value for which r=vr, which corresponds to a length of line equal to The factors .e and (4e-F11) are functions of the frequency. In this 'casethey are linear functions of the same'type as theimpedance of a simple series combination of resistance and inductance, or the admittance of a resistance shunted by a condenser. When the multiplication of the fractions by the initial factors is carried out the elements may be identiied with the impedancesA and admittances of the simple combinations.

The netwerk for the impedance J1 is shown 1n F ig. 2, the desired impedance being that between terminals A and B. VThe first branch is a shunt admittance of value s o E aoz which upon the substitution of the value of .e becomes 1 owLywaos where s LG- t= Jion-LG (17) and This represents the admittance of a capacity of value aos shunted by a resistance (lot.

The remaining shunt Ibranches are ofthe same form, the values of the elements being given by the `products of the'factors s and t and the appropriate coefficient a2, a4, a6, etc. The series branches o f the network likewise compri-ses resistances of respective values alg, agg, etc. in series with inductancesalnaar, etc. where A d r 0R Fs oww- LG l Lo T12' "am 18) The successive shunt resistances are .1 i 1 azt aft etc., and the shunt capacities ags, ais, etc., where J "WELA S "f GR LG and t, U LG E GR LG The numerical design of a network of the 'l type described above for the correction of distortion in any given line requires only the knowledge of the line constants R, L, C and G. The line is preferably divided into a number of sections each of the maximum length given by Equation (16), and a network pr ovided for each section. The schematic system of Fig. 1 shows the networks inserted at intervals along the line, but this is not necessary and the networks may conveniently be grouped together at one end' of the-line. This follows from the fact that the networks have the same characteristic. impedance as the line and consequently may be inserted anywhere 1 without causing wave reflections. The values of the factors Q, r, s and t. 1n the expression R=43 ohms per loop mile L=9X104t henry per loop mile C=6.2X10's farads per mile This corresponds to a number 16 gauge paper insulated telephone cable. The maximum length of line that can befcompensated by a single T-network is found to be 8.8 miles,

in which case o=7r. The resulting structure for J1 is shown in Fig. 6, the values, of the impedance elements being indicated in the drawing. The structure for J2 isY shown in Fig. 7. The first three sections of each network were calculated by the method described above, the remaining sections being added to provide an approximately correct termination. The values of the elements in the end sections were arrived at by'noting that as the line is extended the sections tend towards uniformity. The transmission characteristics of the loading section comprising an 8.8 mile length of uniform line and a compensating r network are illust-'rated by the curves of Figs.

8 and 9. Fig. 8 shows attenuation as a function of frequency; curve 1 represents the attenuation in the line and curve 2 the attenuation in the loadingl section. Fig. 9 shows the di: time of transmission as a function of frequency, curve 3 corresponding to the-line` and curve 4 to the loading section. The compensation is substantially complete except at frequencies below 200 c;p'.s. where there is a slight increase inthe attenuation and a diminution in the time interval. The reason for the residual. distortion is that the attenuation in the ladder structures of the compensating network is small at low frequencies and the waves are able to penetrate to the ends of the structures, where they are reflected.. The residual distortion can be reduced to any desired degree by increasing thernumber of sections,.or by adding` other impedances that will approximateto. an infinite extension.

Other forms of the distortion correcting networks of the invention are shown schematically in Figs. 10 and. 11. The network of Fig. 10 is of the r-type', comprising a^ series branch of impedance Z1 and equal3 shunt branch impedances Z2. The requirements that the network shall have w characteristicl impedanceV equal toAY that of a given line and a propagation constant complementary to that of the linelea'dl to'values of Zland Z2 as follows:

If the same constant values are assigned to a and as in the. case; of the, T`networkthese. equationsl mayA bey rewritten in the forms andL Z2 gef/1+ wat frati-i"- which, upon carrying through the lmultiplication by the initial-factors, Vmay be identified with the impedances of ladder structures ofthe same types as in the T-network. The vr-network is subject to the same limitation as to the length of line that may be compensated as applies to the T-network. This follows from the fact that the expansion of Zl iiivolves the coeilicients mi', al', etc., which become negative for large values of d. Since the expansion for Z2 involves the coei'iicients a0, al, etc., which are always positive, the design of the network for Z2 is not thus restricted.

A type of correcting net-workthat is not subject to this limitation is shown in Fig. 1l. This is the lattice or bridge type having one pair of arms of impedance ZzL and another pair of impedance Zh. In accordancewith the requirements for complete compensation the branch iiiipedances have the values za=z mnh @Ha-rz) 25) and Assuming the same values of a and asbefore, the impedancesZa and Zb are respectively identical with the iinpedances J1 ot the T-network and Z2 of the 7r-network, and may therefore be realized in the ladder type structures already found for these impedances. The design of these networks has already been shown to be free from any restriction as to the value of of, or the length of the line.

In the foregoing analysis the quantities z and a involve the factor (RC-LG), which e may be positive or negative depending on the relative values of the line constants. In almost every practical case the values of the line constants are such that RC is greater than LG, and the only cases in which the magnitudes would be reversed are represented by lines which are impractical either from the economic or from the efficiency standpoint. Even in these cases however, the compensating networks of the invention are applicable. The coeliicients a0, a0', etc., of the various expansions are positive for negative values of u, with the saine limitations as described above, and the factors p, g, p, g', etc., since they involve the product or the quotient of fr and z are also positive regardless of the relative magnitudes of RC and LG. For the particular case RCT-LG the correcting networks disappear, the line being already distortionless.

In the claims which follow the phrase singly infinite is used to describe the ladder networks that constitute the iinpedances of the correcting networks of the invent-ion. This distinguishes from more complicated types in which there is not only an infinite number of-sections but each branch is also constituted by an infinitely extended structure.

What is claimed is: K

l. A distortion correcting network for use with a uniform-transmission line of characteristic impedance Z and propagation constant P, comprising a plurality of branches, each of said branches being constituted by a ladder network including only passive impedance elements, and said ladder networks being initial portions of singly iniinite artificial lines having impedances defined by the product of Z and a -hyperbolic function of (P0;P), where (P0-P) is apropagation constant complementary to l?, whereby the correcting network is adapted to compensate the distortion in the line at all frequencies 2. A distortion correcting network'for use withv a uniform transmission line of characteristic impedance Z and propagation constant P, comprising a plurality of branches each constituted by a ladder network including only passive impedance elements, two of saidl branches being initial portions of singly infinite artificial lines having impedaiices vdefined by f Z mnh (P0-P) ed tov compensate the distortion in the line "l" at all frequencies.

3. A distortion correcting network for use with a uniform transmission line of characteristic impedance Z and propagation constant P, comprising a plurality of branches t each constituted by a ladder networkincluding only passive impedance elements, two of said branches being initial portions of singly infinite artiiicial lines having inipedances de- Yinedby i' where (Pfr-P) is a propagation constant complementary Vto P, and the remaining branches having impedances related thereto whereby the correcting network has the propagation constant (Pf-P), and is adapt- Op the line yteristic impedanceZ and propagation con- :fr

stant P comprising a lattice, or bridge, network, tlie branches of which each comprise a ladder network including only passive impedance elements, one pair of oppositely disposed branches being initial portions ofzo singly infinite artificial lines having impedances defined by ztmmua-P and the other pair having impedances substantially equal to where (Pf-P) is a propagation constant complementary to P, whereby the correcting network is adapted to compensate the distortion in the line at all frequencies.

5. A distortion correcting network of the type set forth in claim 4L in which the propagation constant (P0-P) has such value that the quantity P0, which represents the propagation constant of the distortionless combination of the line and the correcting network corresponds to the attenuation and propagation velocity in the line at infinite frequency.

6. A distortion correcting` network for use with a uniform transmission line having distributed shunt conductance in addition to series resistance and inductance and shunt capacity, said network comprising a`lattice network the branches of which are constituted by ladder type networks including only passive elements, one pair of opposing branches having impedances substantially equal to Z tanh (1)0 -P),

and the other branches having impedances substantially equal to Zwmrm where Z and P' denote respectively the characteristic impedance and the propagation constant of the uniform line, and where (P0-P) is a propagation constant complementary to P, whereby the correcting network is adapted to compensate the distortion in the line at all frequencies.

7. A distortion correcting network in accordance with claim l in which the series branches of the ladder networks are each constituted by a series combination of resistance and inductance, and in which the shunt branches are each formed by a capacity with or without a resistance in shunt thereto.

8. A distortion correcting network for use with a uniform transmission line of characteristic impedance Z and propagation constant P, comprising a T-network, the branches of which each comprise a ladder network including only passive impedance elements, the series branches being initial portions of singly infinite artificial lines having impedances defined by Z sinh (P0-P) and the shunt branches having impedances substantially equal to where (Pf-P) is a propagation constant complementary to P', whereby the correcting network is adapted to compensate the distortion in the line at all frequencies.

In witness whereof, I hereunto subscribe my name this 4th day of December, 1928. THORNTON C. FRY. 

